How do you find the vertices, asymptote, foci and graph #y^2/9-x^2/100=1#?

1 Answer
Narad T.
Nov 6, 2016

The vertices are #(0,3)# and #(0,-3)#
The equations of the asymptotes are #y=3/10x# and #y=-3/10x#
the foci are F#(0,sqrt109)# and F'#(0,-sqrt109)#

Explanation:

The general equation is #(y-h)^2/a^2-(x-k)^2/b^2=1#

This is an up down hyperbola and the center is #(0,0)#

The slope of the asympyotes are #+-3/10#
The equations of the asymptotes are #y=3/10x# and #y=-3/10x#
To determine the foci, we need #c=sqrt(a^2+b^2)=+-sqrt109#
#:.# the foci are F#(0,sqrt109)# and F'#(0,-sqrt109)#
graph{(y^2/9)-(x^2/100)=1 [-18.02, 18.01, -9.01, 9.01]}

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